What you describe is probably what happens here as well. What I described is what an archimandrite told me as he accompanied me to one of these sad proceedings. I got the impression that the adultery requirement was to be tacitly assumed as it was the only reason canonically to grant permisson to remarry. Of course these definitions can get rather confusing as the Church can recognize that a marriage has ended (what it technically does do rather than grant a "divorce") and NOT give permssion to remarry. This however is usually applied if a THIRD marriage fails.